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The multinomial logit model is frequently used in marketing research to explain consumers’ brand choice decisions. In almost all applications of this model, the parameters of the consumers’ utility function are assumed to be constant across time. In contrast to this assumption, both marketing theory and statements from marketing practitioners su...

The multinomial logit model is frequently used in marketing research to explain consumers’ brand choice decisions. In almost all applications of this model, the parameters of the consumers’ utility function are assumed to be constant across time. In contrast to this assumption, both marketing theory and statements from marketing practitioners suggest the possibility of short-term fluctuations and long-term changes in consumers’ brand choice behavior. In this paper, nonparametric brand-specific time-variable functions replace the brand-specific constants usually found in brand choice models. I estimate the model for panel data from two product categories and derive management implications. ; Brand Choice Model; Generalized Additive Model; Multinomial Logit Minimize

We investigate whether the latent class multinomial logit choice model with segmentspecific linear utility functions implies effects that are similar to those of parametric homogeneous nonlinear models given that this latent class model performs at least as well. The two nonlinear models have higher-order polynomial (i.e. quadratic and cubic) an...

We investigate whether the latent class multinomial logit choice model with segmentspecific linear utility functions implies effects that are similar to those of parametric homogeneous nonlinear models given that this latent class model performs at least as well. The two nonlinear models have higher-order polynomial (i.e. quadratic and cubic) and piecewise linear utility functions, respectively. Piecewise linear functions are represented by linear splines and can reproduce threshold, saturation and asymmetric effects. We evaluate models and their variants using a tenfold cross-validation. As criterion we use the geometric mean of choice probabilities across all purchases for the brand actually chosen. We measure the similarity of effects between two models by the absolute differences of choice probabilities implied by these models for varying values of a predictor. Logits of choice probabilities provide a more detailed insight into the effects implied by models. For the data set we analyze, the latent class model with linear utility is clearly superior to the two homogeneous nonlinear models. Overall, the effects implied by the latent class models are similar to those of the two parametric nonlinear models. ; Brand Choice; Latent Class Models; Nonlinear Effects Minimize

Consider a state of a system with several subsystems. The entropies of the reduced state on different subsystems obey certain inequalities, provided there is an equivalence relation, and a function measuring volumes or weights of subsystems. The entropy per unit volume or unit weight, the mean entropy, is then decreasing with respect to an order...

Consider a state of a system with several subsystems. The entropies of the reduced state on different subsystems obey certain inequalities, provided there is an equivalence relation, and a function measuring volumes or weights of subsystems. The entropy per unit volume or unit weight, the mean entropy, is then decreasing with respect to an order relation of the subsystems, defined in this paper. In the context of statistical mechanics a lattice system is studied in detail, and a decrease of mean energy is deduced for blow-up sequences of regular and irregular octogons. Minimize

Consider a state of a system with several subsystems. The entropies of the reduced state on different subsystems obey certain inequalities, provided there is an equivalence relation, and a function measuring volumes or weights of subsystems. The entropy per unit volume or unit weight, the mean entropy, is then decreasing with respect to an order...

Consider a state of a system with several subsystems. The entropies of the reduced state on different subsystems obey certain inequalities, provided there is an equivalence relation, and a function measuring volumes or weights of subsystems. The entropy per unit volume or unit weight, the mean entropy, is then decreasing with respect to an order relation of the subsystems, defined in this paper. In the context of statistical mechanics a lattice system is studied in detail, and a decrease of mean energy is deduced for blow-up sequences of regular and irregular octogons. PACS numbers: 05.50.+q, 03.67.-a, 02.10.Ab 1 Minimize

We study the ground state properties of an atom with nuclear charge Z and N bosonic \electrons" in the presence of a homogeneous magnetic eld B. We investigate the mean eld limit N !1 with N=Z xed, and identify three dierent asymptotic regions, according to B Z 2 , B Z 2 , and B Z 2 . In Region 1 standard Hartree theory is applicable. Region 3 i...

We study the ground state properties of an atom with nuclear charge Z and N bosonic \electrons" in the presence of a homogeneous magnetic eld B. We investigate the mean eld limit N !1 with N=Z xed, and identify three dierent asymptotic regions, according to B Z 2 , B Z 2 , and B Z 2 . In Region 1 standard Hartree theory is applicable. Region 3 is described by a one-dimensional functional, which is identical to the so-called Hyper-Strong functional introduced by Lieb, Solovej and Yngvason for atoms with fermionic electrons in the region B Z 3 ; i.e., for very strong magnetic elds the ground state properties of atoms are independent of statistics. For Region 2 we introduce a general magnetic Hartree functional, which is studied in detail. It is shown that in the special case of an atom it can be restricted to the subspace of zero angular momentum parallel to the magnetic eld, which simplies the theory considerably. The functional reproduces the energy and the one-. Minimize

We study the energy levels of a single particle in a homogeneous magnetic field and in an axially symmetric external potential. For potentials that are superharmonic off the central axis, we find a general “pseudoconcave” ordering of the ground state energies of the Hamiltonian restricted to the sectors with fixed angular momentum. The physical ...

We study the energy levels of a single particle in a homogeneous magnetic field and in an axially symmetric external potential. For potentials that are superharmonic off the central axis, we find a general “pseudoconcave” ordering of the ground state energies of the Hamiltonian restricted to the sectors with fixed angular momentum. The physical applications include atoms and ions in strong magnetic fields. There the energies are monotone increasing and concave in angular momentum. In the case of a periodic chain of atoms the pseudoconcavity extends to the entire lowest band of Bloch functions. 1 Minimize

We study the energy levels of a single particle in a homogeneous magnetic field and in an axially symmetric external potential. For potentials that are superharmonic off the central axis, we find a general "pseudoconcave" ordering of the ground state energies of the Hamiltonian restricted to the sectors with fixed angular momentum. The physical ...

We study the energy levels of a single particle in a homogeneous magnetic field and in an axially symmetric external potential. For potentials that are superharmonic off the central axis, we find a general "pseudoconcave" ordering of the ground state energies of the Hamiltonian restricted to the sectors with fixed angular momentum. The physical applications include atoms and ions in strong magnetic fields. There the energies are monotone increasing and concave in angular momentum. In the case of a periodic chain of atoms the pseudoconcavity extends to the entire lowest band of Bloch functions. Minimize

Thermodynamic stable interaction pair potentials which are not of the form “positive function + real continuous function of positive type ” are presented in dimension one. Construction of such a potential in dimension two is sketched. These constructions use only elementary calculations. The mathematical background is discussed separately. PACS ...

Thermodynamic stable interaction pair potentials which are not of the form “positive function + real continuous function of positive type ” are presented in dimension one. Construction of such a potential in dimension two is sketched. These constructions use only elementary calculations. The mathematical background is discussed separately. PACS numbers: 05.20.-y, 02.20.-a, 02.40.Ft Minimize

We study the energy levels of a single particle in a homogeneous magnetic eld and in an axially symmetric external potential. For potentials that are superharmonic o the central axis, we nd a general \pseudoconcave " ordering of the ground state energies of the Hamiltonian restricted to the sectors with xed angular momentum. The physical applica...

We study the energy levels of a single particle in a homogeneous magnetic eld and in an axially symmetric external potential. For potentials that are superharmonic o the central axis, we nd a general \pseudoconcave " ordering of the ground state energies of the Hamiltonian restricted to the sectors with xed angular momentum. The physical applications include atoms and ions in strong magnetic elds. There the energies are monotone increasing and concave in angular momentum. In the case of a periodic chain of atoms the pseudoconcavity extends to the entire lowest band of Bloch functions. 1 Introduction We consider the non-relativistic quantum mechanical theory of a single particle in a homogeneous magnetic eld and in an external potential. The study of such systems is currently of interest in the context of theories of atoms in strong magnetic elds. In the way of describing the atoms as an assembly of electrons in an eective potential, an essential question is where the e. Minimize